Finite Math Examples

$10 x + 3 > 5 (2 x + 1) - x + 8$

Step 1

Rewrite so $x$ is on the left side of the inequality.

$5 (2 x + 1) - x + 8 < 10 x + 3$

Step 2

Simplify $5 (2 x + 1) - x + 8$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Apply the distributive property.

$5 (2 x) + 5 \cdot 1 - x + 8 < 10 x + 3$

Step 2.1.2

Multiply $2$ by $5$ .

$10 x + 5 \cdot 1 - x + 8 < 10 x + 3$

Step 2.1.3

Multiply $5$ by $1$ .

$10 x + 5 - x + 8 < 10 x + 3$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $x$ from $10 x$ .

$9 x + 5 + 8 < 10 x + 3$

Step 2.2.2

Add $5$ and $8$ .

$9 x + 13 < 10 x + 3$

Step 3

Move all terms containing $x$ to the left side of the inequality.

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Step 3.1

Subtract $10 x$ from both sides of the inequality.

$9 x + 13 - 10 x < 3$

Step 3.2

Subtract $10 x$ from $9 x$ .

$- x + 13 < 3$

Step 4

Move all terms not containing $x$ to the right side of the inequality.

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Step 4.1

Subtract $13$ from both sides of the inequality.

$- x < 3 - 13$

Step 4.2

Subtract $13$ from $3$ .

$- x < - 10$

Step 5

Divide each term in $- x < - 10$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x < - 10$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 10}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 10}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x > \frac{- 10}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $- 10$ by $- 1$ .

$x > 10$

Step 6

Convert the inequality to interval notation.

$(10, \infty)$

Step 7